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Large deviations for quantum spin systems
Mathematical Physics · Submitted 6 Apr 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a self-adjoint element $X$ (level one large deviations).
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The abstract, sentence by sentence
We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a self-adjoint element $X$ (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of $\frac{1}{|\Lambda|}\sum_{i\in\Lambda} \delta_{X_i}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider high temperature KMS states for quantum spin systems on a lattice. | background 0.88 | 0.41 | 0.03 | asserted 0.68 |
| s1 | We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a self-adjoint element $X$ (level one large deviations). | result 0.69 | 0.96 | 0.66 | asserted 1.00 |
| s2 | From the analyticity of the generating function, we obtain the central limit theorem. | result 0.91 | 0.89 | 0.11 | asserted 1.00 |
| s3 | We generalize to a level two large deviation principle for the distribution of $\frac{1}{|\Lambda|}\sum_{i\in\Lambda} \delta_{X_i}$. | contribution 0.52 | 0.94 | 0.28 | asserted 0.99 |
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The paper
Original abstract
We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda|} \sum_{i\in\Lambda} X_i$, where the $X_i$'s are copies of a self-adjoint element $X$ (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of $\frac{1}{|\Lambda|}\sum_{i\in\Lambda} \delta_{X_i}$.
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How the literature uses it
2 arXiv papers cite this in 9 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 2 papers
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Our algorithm is based on combining the abstract cluster expansion for quantum spin systems of Netočný and Redig [ref] with the algorithmic framework of Helmuth, Perkins, and Regts [ref] .
Efficient Algorithms for Approximating Quantum Partition Functions · Introduction · 0.99
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As for quantum systems on a lattice, such as quantum spin systems, we can make use of existing results on the large deviation properties [ref] to prove the thermodynamic bound.
Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems · Quantum spin systems · 0.96
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